Q1) Define the following(Answer Only 10)

1- Law of large numbers:

2- Probability distribution:

3- Sample space:

4- Complementary events:

5- Conditional probability:

6- Random variable:

7- The expected value (mean):

8- Linear combination:

9- Fair game:

10- Random process:

11- General addition rule

Q2)What are the rules for probability distributions?

Q3) Researchers randomly assigned 72 chronic users of cocaine into three groups: desipramine (antidepressant), lithium (standard treatment for cocaine) and placebo. Results of the study are summarized below.

1- What is the probability that a patient relapsed?

2- What is the probability that a patient received the antidepressant (desipramine) and relapsed?

3- If we know that a patient received the antidepressant (desipramine), what is the probability that they relapsed?

4- If we know that a patient relapsed, what is the probability that they received the antidepressant (desipramine)?

Q4) Consider the following (hypothetical) distribution of gender and major of students in an introductory statistics class:

1- The probability that a randomly selected student is a social science major is

2- The probability that a randomly selected student is a social science major given that they are female is